khandy/numpy_utils.py

import numpy as np


def sigmoid(x):
    return 1. / (1 + np.exp(-x))
    
    
def softmax(x, axis=-1, copy=True):
    """
    Args:
        copy: Copy x or not.
        
    Referneces:
        `from sklearn.utils.extmath import softmax`
    """
    if copy:
        x = np.copy(x)
    max_val = np.max(x, axis=axis, keepdims=True)
    x -= max_val
    np.exp(x, x)
    sum_exp = np.sum(x, axis=axis, keepdims=True)
    x /= sum_exp
    return x
    
    
def log_sum_exp(x, axis=-1, keepdims=False):
    """
    References:
        numpy.logaddexp
        numpy.logaddexp2
        scipy.misc.logsumexp
    """
    max_val = np.max(x, axis=axis, keepdims=True)
    x -= max_val
    np.exp(x, x)
    sum_exp = np.sum(x, axis=axis, keepdims=keepdims)
    lse = np.log(sum_exp, sum_exp)
    if not keepdims:
        max_val = np.squeeze(max_val, axis=axis)
    return max_val + lse
    
    
def l2_normalize(x, axis=None, epsilon=1e-12, copy=True):
    """L2 normalize an array along an axis.
    
    Args:
        x : array_like of floats
            Input data.
        axis : None or int or tuple of ints, optional
            Axis or axes along which to operate.
        epsilon: float, optional
            A small value such as to avoid division by zero.
        copy : bool, optional
            Copy x or not.
    """
    if copy:
        x = np.copy(x)
    x /= np.maximum(np.linalg.norm(x, axis=axis, keepdims=True), epsilon)
    return x
    
    
def minmax_normalize(x, axis=None, epsilon=1e-12, copy=True):
    """minmax normalize an array along a given axis.
    
    Args:
        x : array_like of floats
            Input data.
        axis : None or int or tuple of ints, optional
            Axis or axes along which to operate.
        epsilon: float, optional
            A small value such as to avoid division by zero.
        copy : bool, optional
            Copy x or not.
    """
    if copy:
        x = np.copy(x)
    
    minval = np.min(x, axis=axis, keepdims=True)
    maxval = np.max(x, axis=axis, keepdims=True)
    maxval -= minval
    maxval = np.maximum(maxval, epsilon)
    
    x -= minval
    x /= maxval
    return x


def zscore_normalize(x, mean=None, std=None, axis=None, epsilon=1e-12, copy=True):
    """z-score normalize an array along a given axis.
    
    Args:
        x : array_like of floats
            Input data.
        mean:  array_like of floats, optional
            mean for z-score
        std: array_like of floats, optional
            std for z-score
        axis : None or int or tuple of ints, optional
            Axis or axes along which to operate.
        epsilon: float, optional
            A small value such as to avoid division by zero.
        copy : bool, optional
            Copy x or not.
    """
    if copy:
        x = np.copy(x)
    if mean is None:
        mean = np.mean(x, axis=axis, keepdims=True)
    if std is None:
        std = np.std(x, axis=axis, keepdims=True)
    mean = np.asarray(mean, dtype=x.dtype)
    std = np.asarray(std, dtype=x.dtype)
    std = np.maximum(std, epsilon)
    
    x -= mean
    x /= std
    return x


def get_order_of_magnitude(number):
    number = np.where(number == 0, 1, number)
    oom = np.floor(np.log10(np.abs(number)))
    return oom.astype(np.int32)
    
    
def top_k(x, k, axis=-1, largest=True, sorted=True):
    """Finds values and indices of the k largest/smallest 
    elements along a given axis.

    Args:
        x: numpy ndarray
            1-D or higher with given axis at least k.
        k: int
            Number of top elements to look for along the given axis.
        axis: int
            The axis to sort along.
        largest: bool
            Controls whether to return largest or smallest elements
        sorted: bool
            If true the resulting k elements will be sorted by the values.

    Returns:
        topk_values: 
            The k largest/smallest elements along the given axis.
        topk_indices: 
            The indices of the k largest/smallest elements along the given axis.
    """
    if axis is None:
        axis_size = x.size
    else:
        axis_size = x.shape[axis]
    assert 1 <= k <= axis_size

    x = np.asanyarray(x)
    if largest:
        index_array = np.argpartition(x, axis_size-k, axis=axis)
        topk_indices = np.take(index_array, -np.arange(k)-1, axis=axis)
    else:
        index_array = np.argpartition(x, k-1, axis=axis)
        topk_indices = np.take(index_array, np.arange(k), axis=axis)
    topk_values = np.take_along_axis(x, topk_indices, axis=axis)
    if sorted:
        sorted_indices_in_topk = np.argsort(topk_values, axis=axis)
        if largest:
            sorted_indices_in_topk = np.flip(sorted_indices_in_topk, axis=axis)
        sorted_topk_values = np.take_along_axis(
            topk_values, sorted_indices_in_topk, axis=axis)
        sorted_topk_indices = np.take_along_axis(
            topk_indices, sorted_indices_in_topk, axis=axis)
        return sorted_topk_values, sorted_topk_indices
    return topk_values, topk_indices